1. Exponents represent repeated multiplication. For example,
2. More generally, for any non-zero real number a and for any whole number n,In the exponential expression an, a is calledthe base and n is called the exponent.
3. a2 is read as ‘a squared’. a3 is read as ‘a cubed’. a4 is read as ‘a to the fourth power’. ... an is read as ‘a to the nth power’.
4. Homework.
5. Homework.
6. Homework.
7. Homework.
8. 1. All powers of a positive real number a are positive, i.e. for a ∈ R, a > 0, and n ∈ Z, an> 0.2. The even powers of a negative real numbera are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z, (–a)n = an (if n is an even number).3. The odd powers of a negative real number aare negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z, (–a)n= –an (if n is an odd number)
9. The terms of an expression which have the same base and the same exponent are called like terms. We can add or subtract like terms.(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an (a ≠ 0)
10. Let a ∈ R – {–1, 0, 1}(a is a real number other than –1, 0 and 1). If am = an then m = n.
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